If Liebig's law of the minimum was true, why would deficiencies still exist? Thought experiment

[Dennis Wong]

*Liebig's law of the minimum, often simply called Liebig's law or the law of the minimum, is a principle developed in agricultural science by Carl Sprengel (1840) and later popularized by Justus von Liebig. It states that growth is dictated not by total resources available, but by the scarcest resource (limiting factor). The law has also been applied to biological populations and ecosystem models for factors such as sunlight or mineral nutrients. (wiki)

If Liebig's law was true in the strict sense, plants would grow uniformly according to the minimum available resource, and no deficiencies would exist - the fact deficiencies do exist means that plants can grow lacking certain resources by producing flawed/different growth forms. I do think that Liebig's law works in the general sense but plant growth is also affected by hormones and other adaptations.

I think plants also grow with momentum so to say.
Everyone who has run CO2 has seen what happens when it is stopped suddenly. I've seen even water wisteria get algae from CO2 stoppages. Plants like growing at a consistent speed in the short run and dislike sharp disruptions to growth parameters. However, most plants are very adaptable/flexible to a wider range of growth parameters in the long run, but the changes need to be gradual. A poor understanding of this concept has lead many folks to claim that certain plants need XXX to grow well, and that every time XXX drops below a certain level in their tank the plant fails. However, this can easily be due to it being a sharp short term disruption to growth, where as if XXX levels were adjusted slowly, the requirement for XXX could change.

The classic signs of growth momentum being interrupted - plant stress, algae, stunted tips, uneven growth. Many "nutrient deficiency" signs are due to changing/dip in growth momentum - the same plants may adjust to downward nutrient availability given time.

Things that can change tank growth momentum (negatively):

• CO2 stoppages (but not upward spikes it seems?)
• Nutrients level dips
• Nutrient level up spikes (less experienced folks don't realize this)
• Trimming (some species are more resilient than others)
• Replanting/disturbance of substrate zone (especially for substrate fed plants)
• Temperature spikes
• Microbial imbalance ??? (I haven't trashed enough tanks to isolate this)

High growth momentum vs slow growth momentum environments
High growth speed tanks

• Utilize high growth speed, and plant mass to outgrow problems
• Fast feedback, if you do something wrong the signal comes quickly
• However, vulnerable to dips in growth parameters (nutrients, especially CO2)
• Many such tanks end up with overcrowding and aquarist not being able to keep up with overcrowding
• Algae problems can reach escape velocity, making it difficult for less experienced folks to handle
• Seen in Dutch/Plant Collector tanks, tanks that use many fast growers, stem plants

Slow growth speed tanks

• Need to choose which is the limiting factor; CO2? Light? nutrients?
• Plants can become delicate if grown in lean conditions long term, making them vulnerable to even small spikes, easily tipped over
• More reaction time for hobbyists. However, slower feedback loop compared to high growth speed tanks can slow learning.
• Slow plant feedback leaves aquarist wondering if he is doing the right thing
• Excludes certain more demanding species
• Seen in ADA style setups, nature/Iwagumi style aquariums

Working on an article on this and would be happy to hear folk's experiences.

 

[Naturescapes_Rocco]

Great post Dennis. This concept is something that I hope gets more attention with as little misinformation as possible.

Liebig's law is a proven law, but there are so many nuances and caveats dependent on the scenario the plant is in that change HOW we understand this law.

If Liebig's law was true in the strict sense, plants would grow uniformly according to the minimum available resource, and no deficiencies would exist - the fact deficiencies do exist means that plants can grow lacking certain resources by producing flawed/different growth forms. I do think that Liebig's law works in the general sense but plant growth is also affected by hormones and other adaptations.

This (written in bold) is perfect, I would also add something like "hormones, other adaptations, and the interaction of elements on a chemical level within the plant's specific environment".

For example, we're learning that PO4 bound in aquasoil (while chemically the same as PO4 in the water column) does not have the same properties as PO4 in the water column. Or, that too much Ca in the water column can inhibit the uptake of Zn from the water column, but not Zn from aquasoil. Hard to explain that to beginners without overwhelming them, that's the challenge!

The easiest way to provide the "minimum" of what plants need is to use aquasoil, and make sure you also supply some of the required elements in the water column. I think it's extremely difficult (and definitely not beginner friendly) to use inert substrates with water column dosing to grow plants. Which is good, because you're "on brand" for this already!

"The easiest way to fulfill Liebig's Law is to use a good, rich aquasoil, supplemented with liquid ferts." That would be my takeaway for beginners!

The classic signs of growth momentum being interrupted - plant stress, algae, stunted tips, uneven growth. Many "nutrient deficiency" signs are due to changing/dip in growth momentum - the same plants may adjust to downward nutrient availability given time.

Things that can change tank growth momentum (negatively):

• CO2 stoppages (but not upward spikes it seems?)
• Nutrients level dips
• Nutrient level up spikes (less experienced folks don't realize this)
• Trimming (some species are more resilient than others)
• Replanting/disturbance of substrate zone (especially for substrate fed plants)
• Temperature spikes
• Microbial imbalance ??? (I haven't trashed enough tanks to isolate this)

Especially for folks who DO use aquasoil, I think these points are so important. I swear 60% of the issues people actually have are from poor/unstable/low CO2 injection, or too much light relative to the nutrient levels provided (either through aquasoil or liquid ferts). I'm glad you're focusing on these things first before telling people to look for deficiencies.

View attachment 15452

High growth momentum vs slow growth momentum environments
High growth speed tanks

• Utilize high growth speed, and plant mass to outgrow problems
• Fast feedback, if you do something wrong the signal comes quickly
• However, vulnerable to dips in growth parameters (nutrients, especially CO2)
• Many such tanks end up with overcrowding and aquarist not being able to keep up with overcrowding
• Algae problems can reach escape velocity, making it difficult for less experienced folks to handle
• Seen in Dutch/Plant Collector tanks, tanks that use many fast growers, stem plants

View attachment 15451

Slow growth speed tanks

• Need to choose which is the limiting factor; CO2? Light? nutrients?
• Plants can become delicate if grown in lean conditions long term, making them vulnerable to even small spikes, easily tipped over
• More reaction time for hobbyists. However, slower feedback loop compared to high growth speed tanks can slow learning.
• Slow plant feedback leaves aquarist wondering if he is doing the right thing
• Excludes certain more demanding species
• Seen in ADA style setups, nature/Iwagumi style aquariums

View attachment 15449

Working on an article on this and would be happy to hear folk's experiences.

I think it's all great and looks good. Finding a way to explain that Liebig's Law IS a real thing, but that it is affected by water chemistry and nutrient source (active/rich substrates vs inert substrates) as well as countless other factors is an important thing to communicate to people.

For example, Plants literally CANNOT grow if they don't have N, but there are many ways to provide N -- the easiest, by far, is a good, rich substrate. More advanced is providing via liquid or dry ferts.

For 90% of hobbyists, including almost ALL beginners, it's more important to focus on stability, CO2, flow, overall tank cleanliness and light intensity than to worry about Liebig's law of the minimum. But if they can be sure that they have manually removed algae and detritus, perform regular water changes, don't have the light set too strong, and have CO2/flow in check, THEN they should look into how/where their plants are getting their "minimum" nutrients from.

 

[Naturescapes_Rocco]

Also to add (but probably not worth explaining in your article), too much of certain nutrients can make false "deficiencies" appear.

For example, if you dose plenty of Zn, but have way too much Ca (12-16 GH), your plants might exhibit "Zn deficiencies" -- despite dosing "plenty" of Zn.

Same with Fe. If a beginner is dosing 0.5ppm Fe/week, but have PO4 levels in the 10-12 range, they might see Fe-related deficiencies, and have the urge to tell other beginners "you have to dose more than 0.5ppm Fe per week). However, if someone who is running 1ppm PO4/week (or less) like ADA-style tanks was dosing 0.5ppm Fe, they wouldn't see any "Fe deficiencies", and would say that "no one needs anywhere near 0.5ppm Fe/week".

This complexity and nuance is what makes the hobby so damn difficult -- and why nutrient-rich aquasoil changed the game for so many people. I've now seen countless beginners (who literally have no idea what they're doing) be able to "get lucky" and maintain beautiful nano tanks for months without ever dosing ANY ferts, just because they had a thick aquasoil base, and used easy-to-grow plants. No ferts at all! Yet Liebig's Law was still being taken care of, simply because the plants could pull nutrients from the aquasoil for months on end.

 

[Art]

It states that growth is dictated not by total resources available, but by the scarcest resource (limiting factor).

Oh boy, there is so much to think about with good old Leibig’s law. For so many years we used it to minimize PO4 to prevent algae. Good times.

I’m not a fan of using it when thinking about our aquariums. For example, as Dennis mentions, it starts by stating that “growth” is dictated by the scarcest resource. What does that mean? Are we talking about growth speed, health, no growth? How are we defining it?

Scarcest compared to what? Other elements? A certain minimum requirement?

If we have a plant where we are providing enough of all things it needs, does that mean that the one element that is lowest somehow causes a problem? What if too much of one element (e.g., K) causes an uptake problem in the other that is at a normal level?

To me, the point is providing enough of all that a plant needs to grow well being mindful of how nutrient levels can interact with each other. This was @planbrain ‘s thinking with the estimative index. Perhaps he can chime in here.

 

[GreggZ]

Things that can change tank growth momentum (negatively):

• CO2 stoppages (but not upward spikes it seems?)
• Nutrients level dips
• Nutrient level up spikes (less experienced folks don't realize this)
• Trimming (some species are more resilient than others)
• Replanting/disturbance of substrate zone (especially for substrate fed plants)
• Temperature spikes
• Microbial imbalance ??? (I haven't trashed enough tanks to isolate this)

Looks like the start of a great article Dennis. Haven't seen Liebig's law discussed like this in a long time. Back in the day Barr would cite this often and there was plenty of discussion about it.

This last part caught my eye. I've been thinking recently about temperature spikes and microbial imbalance.

I am guessing that large temperature swings can affect beneficial bacteria. I noticed for a while when I was not heating my incoming RO water I would get some problems especially if the source water was really cold. And also plant metabolism slows/rises with temps which could be another issue.

In your experience is temperature stability important? Or something not to really worry about?

And do you think there is an optimal temperature? Or Optimal range? If so what?

 

[Naturescapes_Rocco]

I’m not a fan of using it when thinking about our aquariums. For example, as Dennis mentions, it starts by stating that “growth” is dictated by the scarcest resource. What does that mean?

Don't get too bogged down by the science-jargon of it! I agree that the literal definition isn't great.

Are we talking about growth speed, health, no growth? How are we defining it?

If we were to re-word Liebig's law to more understandable language, it would be that a plant can only grow as much as the most limiting ingredient is present.

Scarcest compared to what? Other elements?

Yes, at the ratio that they're consumed alongside each other.

A certain minimum requirement?

Technically, yes!

I always explain Liebig's law using my "cake factory" analogy.

Think of plants, on a cellular level, as a solar-powered cake factory. Trying to make cakes all day while the sunshine is powering the factory.

To make just one cake, you need 30 flour, 10 sugar, 4 eggs, 2 vanilla, 1 salt.

Question: If the factory has 10000 flour, but no sugar, how many cakes can it make?

Answer: None! The cake production is limited by the most limiting ingredient.

This is the basic point of Leibig's law. It's not a theory, it's a proven concept particularly in plant growth. It's often a cause of algae in our plants; if you have plenty of NO3 and PO4, but little to no K, your plants will stall and algae will grow.

If we have a plant where we are providing enough of all things it needs, does that mean that the one element that is lowest somehow causes a problem?

This is where it gets more nuanced and complicated, and where we have to look at specific scenarios more closely.

For example, take Calcium. Plants uptake very little of it (less than 0.1ppm/day in heavily planted tanks?), but you will have serious issues if you only provide 5ppm Ca in the water column.

"But why? Isn't 5ppm more than zero ppm?" Yes! So while technically you haven't let ppm Ca reach zero, there's sometimes more to it than that.

In the calcium example, plants don't have active mechanisms for manually absorbing calcium by default; they essentially rely on a certain concentration of Ca to "push" into their cells. So, if the water column has 20-30ppm Ca, plants are usually plenty happy -- despite only consuming very little each week. In this Calcium case, Leibig's Law would almost be more like the "scarcity point/minimum" is 20ppm Ca, where anything lower than that creates a scenario where Ca is now the limiting ingredient, and plants will be unable to grow properly.

What if too much of one element (e.g., K) causes an uptake problem in the other that is at a normal level?

The simple answer is that if too much K is causing Mg to not be consumed, then yes, the plant will suffer because of the lack of Mg due to Liebig's Law. Yes, it's indirectly because of too much K -- but the real reason is because of K being the limiting ingredient.

This is why "scarcity" is sometimes a poor choice for the definition of the concept; it should simply be the "limiting ingredient".

Here's the big takeaway:​

• Whether that ingredient is limited because it has reached zero (in the case of NO3, for example)...
  
  
• Whether that ingredient is limited because there isn't enough in the water column to be useful (in the case of 5ppm Ca, for example)....
  
  
• Whether that ingredient is limited because too much of second element is inhibiting the uptake of the first ingredient (in the case of too much K inhibiting Mg)...

... The plant's growth will be limited, or stop completely, due to Liebig's Law. Simple as that! It's all the potential situations that get complicated.

It's most useful to explain to beginners that they either need an aquasoil substrate, or they need to fertilize weekly, or both... but their plants won't grow (or will grow algae) if they just do nothing. Plants need food, and usually rely on us to feed them.

---

And in our aquariums, when plants stop growing, algae takes it's place.

In the cake factory analogy, algae is bread. It only needs salt and flour. So if you're missing eggs, you can't make a cake -- but you can make bread, and we don't WANT bread -- we want cakes.

To me, the point is providing enough of all that a plant needs to grow well being mindful of how nutrient levels can interact with each other. This was @planbrain ‘s thinking with the estimative index. Perhaps he can chime in here.

Agreed! But sometimes it can be useful to use Liebig's Law to explain this concept.

Whether through water column dosing, fish waste, root tabs, or a nutrient-rich substrate, if plants don't have the minimum they need of ANY nutrient, they just cannot grow.

 

[ElleDee]

If you are talking deficiencies/toxicities, I think this generalized graph is more useful:


I've seen many versions of the above, I just grabbed this one off the internet randomly. Liebig's law is good for thinking about plant nutrients in relation to each other, were deficiencies/intoxicates are specific to the status of a particular nutrient. Neither concepts really address the growth issues we see with dips/spikes in nutrient availability. Whatever you do, don't include Mulder's chart. Unless you put a big X over it and tell the kids at home to throw it in the garbage.

 

[GreggZ]

This was @planbrain ‘s thinking with the estimative index. Perhaps he can chime in here.

Oh boy I hope he does this should get good!

 

[JayP]

 

[Art]

@plantbrain

 

[GreggZ]

Also to add (but probably not worth explaining in your article), too much of certain nutrients can make false "deficiencies" appear.

For example, if you dose plenty of Zn, but have way too much Ca (12-16 GH), your plants might exhibit "Zn deficiencies" -- despite dosing "plenty" of Zn.

Same with Fe. If a beginner is dosing 0.5ppm Fe/week, but have PO4 levels in the 10-12 range, they might see Fe-related deficiencies, and have the urge to tell other beginners "you have to dose more than 0.5ppm Fe per week). However, if someone who is running 1ppm PO4/week (or less) like ADA-style tanks was dosing 0.5ppm Fe, they wouldn't see any "Fe deficiencies", and would say that "no one needs anywhere near 0.5ppm Fe/week".

This complexity and nuance is what makes the hobby so damn difficult -- and why nutrient-rich aquasoil changed the game for so many people. I've now seen countless beginners (who literally have no idea what they're doing) be able to "get lucky" and maintain beautiful nano tanks for months without ever dosing ANY ferts, just because they had a thick aquasoil base, and used easy-to-grow plants. No ferts at all! Yet Liebig's Law was still being taken care of, simply because the plants could pull nutrients from the aquasoil for months on end.

LOL another discussion we used to have often.

So might as well throw Mulder's Chart into this discussion.

Then that will lead to ratios.

If people thought we were nerding out before they have no idea!

 

[ElleDee]

LOL another discussion we used to have often.

So might as well throw Mulder's Chart into this discussion.

Then that will lead to ratios.

If people thought we were nerding out before they have no idea!

View attachment 15473

I repeat, throw this in the garbage! I tried to go back and see where this came from at one point, and it's ancient and obscure. Not a real, validated thing. Throw it awaaaaaay.

 

[JacksonL]

LOL another discussion we used to have often.

So might as well throw Mulder's Chart into this discussion.

Then that will lead to ratios.

If people thought we were nerding out before they have no idea!

View attachment 15473

Mulders chart seems to have a real cult following too. Cult being the right word too as it is certainly preached as a gospel.

 

[Koan]

Not a real, validated thing. Throw it awaaaaaay

a real cult following too. Cult being the right word

<GEEK>

Mulder published his observations in 1953, as a way to engender discussion about the complexity involved in soil nutrition in land agriculture

▷ Muller diagram - Nutrient relationships (Updated)

Discover nutrient interactions with Mulder's Diagram. Improves soil health and plant growth

www.tiloom.com

The complexities are compelling, of course, and have been refined continuously since then in many interesting - although much less visually lovely - ways

https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2021.663477/full

All critical in food agriculture where minuscule changes in inputs can make or break the success of food crops

Being as weeds are not algae, aquariums are not hectares of arable land, and far and away the primary stressors for underwater plants are access to consistent carbon and to general environmental stability.. the comparison becomes a little silly

</GEEK>

 

[That Guy Brian]

This thread has successfully made my brain hurt lol

-B

 

[ElleDee]

<GEEK>

Mulder published his observations in 1953, as a way to engender discussion about the complexity involved in soil nutrition in land agriculture

▷ Muller diagram - Nutrient relationships (Updated)

Discover nutrient interactions with Mulder's Diagram. Improves soil health and plant growth

www.tiloom.com

The complexities are compelling, of course, and have been refined continuously since then in many interesting - although much less visually lovely - ways

View attachment 15482

View attachment 15483

https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2021.663477/full

All critical in food agriculture where minuscule changes in inputs can make or break the success of food crops

Being as weeds are not algae, aquariums are not hectares of arable land, and far and away the primary stressors for underwater plants are access to consistent carbon and to general environmental stability.. the comparison becomes a little silly

</GEEK>

It's not that nutrient interactions don't exist, but it's complicated. It's even harder to meaningfully deploy and I have no idea how to apply the concepts in an aquatic enviroment where there's both foliar and root uptake to contend with. Even that top chart you reposted looks like Mulder's chart in that it has elements with arrows that point at each other, the arrows represent interactions resulting from single-element deficiency, not synergistic or antagonistic relationships generally. It's not the same thing. (You didn't say they were the same, @Koan, I'm just commentating for anyone who is just taking a quick glance.) And it doesn't agree with Mulder's chart for many of the interactions anyway!

There were other researchers contemporaneous to Mulder who were doing similar research in interactions. It may have even been good work for the time, but good luck finding the original data! Nevertheless, that research thread has continued and it's kind of insulting to modern agricultural research to roll this dusty graphic out and point to it like it's gospel. It's not like there aren't foundational plant science concepts that were discovered long ago, but if they are important and have held up they make it into textbooks and are cited in current publications. Mulder's chart has found a following in some niche corners of the plant world (such as our hobby), but it's not the current state of the science.

I have ranted about this in 2022 at TPT, in 2024 at UKAPS, and now here in 2026. I don't think anyone has cared even a tiny bit about my hot take on Mulder's chart, but you know, it feels good to let out my annoyance every now and again. I'll be ready to have a go again in 2028.

 

[Aquajack]

...and here I thought Fox Mulder had a career before The X Files although a couple of those lasts charts from Koan do look a little alien

 

[GreggZ]

I have ranted about this in 2022 at TPT, in 2024 at UKAPS, and now here in 2026. I don't think anyone has cared even a tiny bit about my hot take on Mulder's chart, but you know, it feels good to let out my annoyance every now and again. I'll be ready to have a go again in 2028.

@ElleDee I did not mean for that post to be triggering!!

As you know this one comes up every so often and always seems to creates a stir. Some hold it as gospel, and others as nonsense. Maybe the truth is somewhere in between? Who knows?

But it's always good for a hot debate! That's been true for a couple of decades.

It's the same with charts like this..............they will keep coming up forever!

 

[ElleDee]

@ElleDee I did not mean for that post to be triggering!!

As you know this one comes up every so often and always seems to creates a stir. Some hold it as gospel, and others as nonsense. Maybe the truth is somewhere in between? Who knows?

But it's always good for a hot debate! That's been true for a couple of decades.

It's the same with charts like this..............they will keep coming up forever!

View attachment 15511

Nah, I love a good rant every now and then!

I don't love the use of those nutrient deficiency charts either, but that's more of a situation where it's just enough information to get people into trouble rather than being flat wrong. There are generalized deficiency symptoms that can give a helpful starting point for figuring out problems, but it's best paired with a lot of background knowledge and that's much harder to come by.

 

[JacksonL]

It's not that nutrient interactions don't exist, but it's complicated. It's even harder to meaningfully deploy and I have no idea how to apply the concepts in an aquatic enviroment where there's both foliar and root uptake to contend with. Even that top chart you reposted looks like Mulder's chart in that it has elements with arrows that point at each other, the arrows represent interactions resulting from single-element deficiency, not synergistic or antagonistic relationships generally. It's not the same thing. (You didn't say they were the same, @Koan, I'm just commentating for anyone who is just taking a quick glance.) And it doesn't agree with Mulder's chart for many of the interactions anyway!

There were other researchers contemporaneous to Mulder who were doing similar research in interactions. It may have even been good work for the time, but good luck finding the original data! Nevertheless, that research thread has continued and it's kind of insulting to modern agricultural research to roll this dusty graphic out and point to it like it's gospel. It's not like there aren't foundational plant science concepts that were discovered long ago, but if they are important and have held up they make it into textbooks and are cited in current publications. Mulder's chart has found a following in some niche corners of the plant world (such as our hobby), but it's not the current state of the science.

I have ranted about this in 2022 at TPT, in 2024 at UKAPS, and now here in 2026. I don't think anyone has cared even a tiny bit about my hot take on Mulder's chart, but you know, it feels good to let out my annoyance every now and again. I'll be ready to have a go again in 2028.

Rant away! Love reading a rant where I learn something at the same time